I know that is an odd statement to make when it cost us 2 days of our cruise. But we have been to Cozumel 100 times and we were not even going to get off the ship in Progresso...so we did not miss a thing!!
Embarkation was very easy for us. We waited in the air-conditioned section where the folks were getting OFF...until they opened the door. Then when the first group escorted to the holding room (also A/C), a Carnival Rep came and got us and took us in also.
We had VIP Check In once we got indoors...so it was fairly quick (once they started checking in) and we were on the ship.